Timed signals received by a receiver/processor from satellites are now routinely used to determine location coordinates and/or receiver time offset of the receiver. Two examples of this are the signals received as part of a Global Positioning System (GPS), signals received as part of a Global Orbiting Navigational Satellite System (GLONASS), and signals received as part of a Low Earth Orbit (LEO) system, such as the 66-satellite Iridium constellation proposed by Motorola.
One potential problem here is that the minimum number of satellites needed for determination of location coordinates alone (usually two or three) or for determination of location coordinates and receiver time offset (four) may not be in view simultaneously. A related problem occurs for an extraterrestrial exploration vehicle, such as the landing vehicle for the Mars Explorer that touched down on that planet's surface on or around Jul. 3, 1997, wherein only a single satellite, the mother ship orbiting the planet, is available to provide timed signals for location determination.
The U.S. Navy Navigation Satellite System, also known as "Transit," used triangulation from signals received from a plurality of satellites with orbits in polar planes to estimate a user's location. Development of the Transit system began at Johns Hopkins in 1958, became partly operational in 1963 and became fully operational in 1968. The Transit system included at least six satellites, arranged in polar orbits (angle of inclination relative to the equator=90.degree.), with altitudes of about 1075 kilometers (km) above the Earth's surface with orbit time intervals of 107 minutes. The six orbits formed a "bird cage" constellation around the Earth. The average time between usable satellite passes was about 90 minutes, but the actual time can vary between 30 minutes and several hours, depending upon the observer's location.
Each satellite transmitted signals at each of two frequencies, 150 MHz and 400 MHz, with a frequency stability of about 1 part in 10.sup.11. The transmitted signal includes a navigation message that is repeated every two minutes. The navigation message itself was updated every 12 hours but could run for up to 16 hours without requiring an update. The Transit ground support system included four tracking stations within the U.S., plus two signal injection stations to inject navigation message updates and a computer center that created the message update. The navigation message included a fixed part with geometrical parameters that describe a perfectly smooth elliptical orbit and a variable part that provides corrections to the elliptical orbit parameters; every two minutes, a new orbital correction is added and an older correction is deleted.
The signal frequency transmitted at 400 MHz (nominal) by each Transit satellite was offset by 32 kHz to provide a relatively low frequency difference (32 kHz.+-.8 kHz) after mixing the received signal (f=F.sub.G) with a 400 MHz signal (f=F.sub.R) at a ground station. The distance or slant range of a given Transit satellite from a ground-based user was determined using a carrier phase count of the number of full and partial cycles N received between two selected time markers t1 and t2, viz. EQU N=(F.sub.G -F.sub.R)dt=(F.sub.G -F.sub.R)(t2-t1)+F.sub.G (R2-R1)/c, (1)
where R1 and R2 are the as-yet-unknown distances of the satellite from the user at the beginning and end of the integration interval, respectively. The change in slant range, R2-R1, was determined from the Doppler shift change, represented by the last term in Eq. (1). Each full count (.DELTA.N=1) of a carrier phase signal represents about 0.75 meters. Two frequencies, 150 MHz and 400 MHz, were used to estimate the time delay due to signal propagation in the ionosphere. Time delay due to signal propagation in the troposphere and due to refraction was estimated as a unit. For this dual frequency set, the estimated maximum radial error and rms radial error for location using the Transit system are about 77 meters and 32 meters, respectively. A computer uses a least square error approach to estimate the best fit of location, based upon the Doppler shift signals determined for each of the two or three visible satellites. If the user moves during the time interval of receipt of the signals transmitted by the satellites, the system requires accurate specification of the velocity vector during this interval and usually relies upon dead reckoning between location fixes.
The Transit system is discussed by Gueir and Weiffenbach, "A Satellite Doppler Navigation System", Proc. I.R.E. (1960) pp. 507-516, and by Williams, "Marine Satellite Navigation Systems", SERT Journal, vol. 13 (1977) pp. 50-54.
The Transit system required fixed inclination angles for each of a collection of satellites, used a least square error approach, rather than an exact analytical approach, to determine user location, did not explicitly account for the rotation of the Earth, relying instead on simultaneous visibility of two or three satellites, and relied upon dead reckoning to determine user location between location fixes.
What is needed is an approach that allows receipt and analysis of fewer (as few as one) than the theoretical minimum number of (simultaneous) satellite signals needed, to determine the location coordinates and/or receiver time offset (referred to collectively here as "location fix coordinates") for a receiver. Preferably, the approach should be flexible and should allow (1) receipt and analysis of signals from as few as a single satellite and (2) receipt and analysis of signals from satellites that are part of different location determination (LD) systems ("mixed system signals"), such as a mixture of GPS and LEO signals or a mixture of GPS and GLONASS signals.